The bishop and knight checkmate is the trickiest of the basic mates: with just a bishop, a knight and the king you must drive the enemy king into a corner of the bishop’s colour.
King, bishop and knight can force mate against a lone king, but only by herding it into one of the two corners the bishop controls. The other two corners are safe, so the technique is about steering the king the right way.
Because it can take many precise moves and the fifty-move clock is ticking, this mate has a reputation as the hardest of the elementary endings. The standard method uses the bishop, knight and king together as a coordinated net, often via a ‘W’ knight manoeuvre.
It’s rare in practice but worth knowing, both to win it and to defend it (by fleeing toward the ‘wrong’, safe corner). The final picture is always the king trapped in a corner the bishop can attack.
You can only mate in the two corners the bishop’s colour can reach, so you must steer the king there while keeping all three pieces coordinated — all within the fifty-move limit. It takes precise technique.
A corner the same colour as the bishop’s squares. A light-squared bishop mates on a light corner (a8 or h1); a dark-squared bishop mates on a dark corner (a1 or h8). The other two corners are safe for the defender.
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